{"paper":{"title":"On the Initial-Boundary Problem for the Time-Fractional Diffusion Equation in the Quarter Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Demian Goos, Eduardo Santillan Marcus, Gabriela Reyero, Sabrina Roscani","submitted_at":"2013-06-07T15:24:33Z","abstract_excerpt":"Taking into account the asymptotic behavior of some Wright functions and the existence of bounds for the Mainardi and the Wright function $W(-x,\\frac{\\alpha}{2}, 1)$ in $\\mathbb{R}^+$ , three different initial-boundary-value problems for the time-fractional diffusion equation in the quarter plane, where the time-fractional derivative is taken in the Caputo sense of order $\\alpha$ $\\in (0,1)$ are solved. Moreover, the limit when $\\alpha \\nearrow 1$ of the respective solutions are analyzed, recovering the respective solutions of the classical boundary-value problems when $\\alpha=1$ and the fract"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1748","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}